You can meet with a lot of disappointment if your painting project doesn't turn out the way you want it to. Especially, when you end up painting the things you weren't supposed to. Yes, spilling a few droplets on your new carpet is definitely a nightmare. Simple cleaning won't always help, particularly if the stain is stubborn.
Actually, covering the area with newspapers, before painting is a good idea to prevent droplets from falling. But, if the damage has already been done, you have no choice but to resort to the damage control methods to save your carpet from getting permanent stains.
Before going for any stain removal method, assess the damage done. Be practical in your approach. Attempting to remove the stains is a feasible option only when they cover a small portion of the carpet. In case you have knocked down the entire bucket of paint on it, there is little you can do to salvage it.
In such cases, you should inquire if your home insurance company covers accidental damage due to paint. In other cases, simply identify the type of the paint to decide what kind of cleaning is required.
You can determine the type by reading the 'brush cleaning instructions' mentioned on the paint bucket. If it mentions water and soap solution for cleaning, then the paint is water soluble. If it says turpentine or white spirit, then it is oil based.
Once you have removed the excess paint, rub the stain with a soap solution. If the stain doesn't dissolve, you need to soak it for a few minutes. Blot it with a napkin or a damp cloth. Do not rub it, and always use blotting motions to get rid of it.
The process of removing them remains the same as that of water soluble paint, only instead of soap solution use the solvent. While blotting, make sure you don't spread the stain and worsen the damage.
Remove paint with extreme care as there is often a chance of damaging the carpet. If the area occupied by the stain is too much, use a special carpet cleaner, depending upon the type of your carpet. Do rely on a professional help if need be. Good luck!